Model for a biexciton

Model for a biexciton in a lateral quantum dot based on exact solutions for the Hookean H2 molecule. I. Theoretical aspects
E.V. Lude˜ aa ,∗ L. Echevarr´ b , J.M. Ugaldec , X. Lopezc , and A. Corella-Madue˜ od . n ıa n
a Centro

de Qu´mica, Instituto Venezolano de Investigaciones Cient´ficas, IVIC, Apartado 21827 ı ı Caracas, Venezuela

b Departamento c Kimika

de Qu´mica, UniversidadSim´n Bol´var, Sartenejas, Caracas, Venezuela ı o ı

Fakultatea, Euskal Herriko Unibertsitatea and Donostia International

Physics Center, Posta Kutxa 1072, 20080 Donostia, Euskadi, Spain
d Departamento

de F´sica, Universidad de Sonora, Apartado Postal 1626 ı Hermosillo, Sonora, M´xico. e (May 2, 2011)

Abstract We present here a model for the non-Born-Oppenheimer description of thebiexcitonic complex X2 (eehh) trapped in laterally-coupled quantum dot system. We define a zerothorder Hamiltonian which allows us, under certain conditions on the masses and coupling constants, to decouple the problem. We show that the zeroth-order wavefunctions and energies can be described using the exact solutions for the Hookean model for the H2 molecule [J. Chem. Phys. 123, 024102 (2005)]. We alsoapply this Hookean model to the description of the excitonic complexes X+ (ehh), X− (eeh), and to the single exciton X(eh) and analyze the 2 dependence of the total non-Born-Oppenheimer zeroth-order energies, and binding energies for these sytems with the mass ratio σ. The general features of the results obtained using

∗ Corresponding

Author, email:popluabe@yahoo.es. Publicado en Inter. J.Quantum Chem. 111,

1808-1818 (2011)

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this Hookean model agree quite well with those of more elaborate calculations.

I. INTRODUCTION

Coupled semiconductor quantum dots are novel structures that have attracted much attention because of their potential applications in quantum cryptography and quantum computation.[1–5] Much progress has been achieved in the fabrication and control ofproperties of vertically stacked quantum dots[6–9] as well as of laterally coupled ones.[10–15] A first-principle’s theoretical treatment of these structures (comprising over 5000 atoms) has been carried by Jaskolski et at.[16] For a review of application of simpler models to lateral quantum dots in a magnetic field, see Helle et al.[17, 18] The effects of exciton splitting of two laterally coupledquantum dots under the influence of an electric field are of particular interest.[19] This is due to the important role that an electrically tuned lateral quantum dot could play in the development of controllable quantum gates, which are the basic elements for the realization of quantum computers.[15, 20–22] On the other hand, it has been experimentally demonstrated that the type of coupling of lateralquantum dots has a definite expression in the photoluminiscence spectrum and, hence, it would be desirable to attain understanding of this phenomenon for the purpose of having a voltage-controlled emission of non-classical light.[15, 23] The latter is an essential feature in many areas having to do with the development of opto-electronic devices.[24] The importance of excitons for determining theoptical properties in semiconductor nanocrystals is already well known.[25, 26] The presence of biexciton states in semiconductor quantum dots was experimentally demonstrated (and theoretically corroborated) by Hu in 1990.[24] In a single quantum dot, different pathways leading to the formation of excitons have been studied[27] and coherent optical control of biexcitons has been experimentallyachieved.[28] Calculations have been performed to determine the binding energies of exci-

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tonic complexes as a funtion of the quantum dot hight[29] and length.[30] Also, the size of quantum dots in which biexcitons are generated under a two-photon resonant excitation, has been determined.[31] In a coupled lateral quantum dot, the important interactions are of the exciton-exciton type.[32]...